One of the most popular methods for measuring the mass flow rate of media moving through a conduit is to generate a flexural vibration of the circuit in a symmetric mode about the midsection of the conduit, and measure the phase angle different in the flexural vibration between the two opposite halves of the conduit or measure the asymmetry in the flexural vibration about the mid-section of the conduit as a measure of the mass flow rate of the media. At the present time, this method of measuring the phase angle difference or measuring the asymmetry in the flexural vibration is being practiced with the embodiments of the conduits shown in FIGS. 13 through 17. The inventor of the present invention, Hyok S. Lew has invented a number of different embodiments of the mass flowmeter employing one or a pair of vibrating conduits, shown in FIGS. 1 through 6 and 8 through 11, which combinations having unique structural features require a unique method for analyzing the flexural vibration of the conduit in determining the mass flow rate of media moving therethrough.